I haven't seen it posted about the chief have a baby. Mine did by accident,,,,,will she be the next chief,,,,,or is there nothing special about the baby???

No. There's nothing special about the baby. His or her chances of becoming chief later on are the same as those of any other villager.

In the early part of the game, if my chief is a woman, I often use her as a mother, to save taking a worker away from her duties for a couple of years.

She can also heal, just figured that out!!